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We need to wrap up this cube-shaped present, remembering that we
can have no overlaps. What shapes can you find to use?

Cube Drilling

Stage: 2 Challenge Level:

Well done to all of you who sent in solutions to this problem - there are too many to mention you all, I'm afraid. Not so many of you answered both parts of the question, though! Mrs Alford's Maths Challenge Group at West Lodge Middle School, Mathew and Sam from Woodfall Primary and Linden from Comberton Village College explained their thinking clearly. West Lodge
pupils say:

40 cubes were not drilled.
By drilling a hole in each corner of the face that is facing you, you get 16 cubes that have been drilled through.
When the friend drills through, 2 cubes on each edge have already been drilled so they don't count.
A total of 8 extra cubes have been drilled.
So 8 + 16 = 24 (cubes drilled.)
So 64 - 24 = 40 not drilled.

Sakib from Swanlea School sent us a picture which really helps the visualisation:

William from St Patrick's School found a solution to the second part of the problem too:

If you were to drill through the centre 4 cubes (that are also 4 cubes deep) then 4 cubes x 4 cubes = 16.
Than if you drilled down from the top, only 2 cubes would have new holes
4 x 2 = 8, 8 + 16 = 24, 64 - 24 = 40.

The NRICH Project aims to enrich the mathematical experiences of all learners. To support this aim, members of the
NRICH team work in a wide range of capacities, including providing professional development for teachers wishing to
embed rich mathematical tasks into everyday classroom practice. More information on many of our other activities
can be found here.